I bet you need to check the individual entry of each super heavy vehicle. The BrB explains the basic rules for super heavies and the actual model entry should add/clarify their rules. That being said the super heavy always fires all it's weapons, even ordinance, when it moves and can fire them at all different targets.

How far it can move? The super heavy entry does not say it has the heavy special rule which would limit its movement speed to 6". Some people might argue the word heavy is in its title and should follow the heavy rule, but it's already except from that rule in shooting.

I guess a super heavy vehicle can move just like any other vehicle. Up to 12" a turn, but since it's a super heavy it can always fire all it's guns to full effect. So 12" movement and fire away.